A Breif History Of Zero

A Breif History Of Zero

Initially, the zero as a number was not available. There was the idea of empty space, which may be thought of conceptually as similar to zero. Babylonians around 700 BC used three hooks to denote an empty place in the positional notation. They used a symbol sort of like a “Y” for one, and a symbol sort of like “<” for ten.

Greek mathematicians made some unique contributions to mathematics. The interesting feature is that Greek mathematics is mostly based on geometry. Euclid wrote a book on number theory named Elements, but that was completely based on geometry. The newer system of Greek mathematics, which is more than 2000 years old, used Greek letters for 1 to 9, 10 to 90, and 100 to 900.  1 was written as ‘A’ (alpha), 10 as ‘I’ (iota), and 100 as ‘Π’ (rho). They did use a limited place system, so ‘111’ was written as ‘ΠIA’.  For 1000 and above they used a mark such as ‘,’ or ‘/’ before the number of thousands.  So, ‘1000’ is ‘,A’ or ‘/A’ , and ten thousand is ‘,I’ or ‘/I’.

Greek astronomers might have felt the need for empty space and began to use the symbol ‘O’. It is not clear why they favoured the particular notation. It may be related with the first letter of the Greek word for nothing namely  ouden or it may come from  obol, a coin of almost no value.

Roman numerals for 1, 10, 100, and 1000 are I, X, C, and M. It is interesting that Greeks or Romans relied more on the Abacus that they used to perform arithmetic operations such as addition, subtraction, division, or multiplication and they may not have thought of any operation related with zero. in early history of most of Greek and Roman civilisations, there is no concrete evidence of zero or its use. This may be due to conceptual difficulty to figure out something, which would represent nothingness.

Aryabhata

Around AD 650, the use of zero as a number came into Indian mathematics. The Indians used a place value system and zero was used to denote an empty place. In fact there is evidence of an empty placeholder in positional numbers from as early as AD 200 in India.  Around AD 500 Aryabhata devised a number system, which had no zero as a positional system, but used it to denote empty space. There is evidence that a dot had been used in earlier Indian manuscripts to denote an empty place in positional notation. For example, to represent ‘100’ it would be two dots after 1.

In AD 628, Brahmagupta wrote  Brahmasphutasiddhanta (The Opening of the Universe), and attempted to give the rules for arithmetic involving zero and negative numbers. He explained that given a number, if you subtract it from itself you obtain zero. He gave the following rules for addition, which involve zero: The sum of zero and a negative number is negative, the sum of a positive number and zero is positive; the sum of zero and zero is zero. Similarly, he gave the correct rules for subtraction also.

Brahmagupta then said that any number when multiplied by zero is zero, but when it comes to zero, he gave some rules that were not correct. But remember, when the concept was just developing, it is quite usual that he would make mistakes. So it was an excellent attempt to visualise number system in the light of negative numbers, zero and positive numbers.

In AD 830, Mahavira wrote Ganita Sara Samgraha (Collections of Mathematics Briefings), which was designed as an update of Brahmagupta’s book. He correctly stated the multiplication rules for zero, but again gave incorrect rule for division by zero.

Bhaskara

After 500 years of Brahmagupta, Bhaskara tried to solve the problem of division by stating that any number divided by zero as infinity. Well, conceptually though it is still incorrect, but Bhaskara did correctly state other properties of zero, such as square of zero is zero and square root of zero is also zero. So Indian mathematicians developed the concept of zero and stated different mathematical operations involved with zero.

The Islamic and Arabic mathematicians took the ideas of the Indian mathematicians to further west. Al-Khwarizmi described the Indian place value system of numerals based on zero and other numerals. Ibn Ezra, in the 12th century, wrote The Book of the Number, which spread the concepts of the Indian numeral symbols and decimal fractions to Europe.

In 1247 the Chinese mathematician Ch’in Chiu-Shao wrote  Mathematical Treatise in Nine Sections, which used the symbol ‘O’ for zero. In 1303, Chu Shih-Chieh wrote Jade Mirror of the Four Elements, which again used the symbol ‘O’ for zero.

Leonardo Fibonacci

In around 1200, Leonardo Fibonacci wrote  Liber Abaci where he described the nine Indian symbols together with the sign ‘0’. However, the concept of zero took some time for acceptance. It is only around 1600 that zero began to come into widespread use after encountering a lot of support and criticism from mathematicians of the world.

The word zero probably came from the Sanskrit word for  shunyam or the Hindi equivalent of  shunya. The word  shunyam was translated to Arabic as al-sifer. Fibonacci mentioned it as cifra from which we have obtained our present cipher, meaning empty space. From this original Italian word or from alteration of Medieval Latin zephirum, the present word zero might have originated.